Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

Micromachining of circular ring microstructure by femtosecond laser pulses

In this paper, integration of interference phenomenon into femtosecond laser micromachining was reported as the femtosecond laser pulses were reshaped spatially to perform ablation. The generation of circular interference pattern was demonstrated by overlapping infrared femtosecond laser pulses. The interference pattern was subsequently focused on a copper substrate to ablate microstructures of concentric circular rings. The present technique is expected to open up new applications in the areas of rapid fabrication of micro-Fresnel lenses, hybrid microlenses and lens arrays.     

1,3-dihalo-5,5-dimethylhydantoin/NaNO2 as an efficient heterogeneous system for the N-nitrosation of N,N-dialkylamines under mild conditions

A combination of 1,3-dihalo-5,5-dimethylhydantoin (X = Br, Cl) and sodium nitrite in the presence of wet SiO₂ was used as an effective nitrosating agent for the nitrosation of N,N-dialkyl amines to their corresponding nitroso derivatives under mild and heterogeneous conditions in good to excellent yields.     

A short note on the entrainment and exit boundary conditions

An attempt is made to find out the suitable entrainment and exit boundary conditions in laminar flow situations. Streamfunction vorticity formulation of the Navier–Stokes equations are solved by ADI method. Two‐dimensional laminar plane wall jet flow is used to test different forms of the boundary conditions. Results are compared with the experimental and similarity solution and the proper boundary condition is suggested. The Kind 1 boundary condition is recommended. It consists of zero first derivative condition for velocity variable and for streamfunction equation, mixed derivative at the entrainment and exit boundaries. Copyright © 2005 John Wiley & Sons, Ltd.     

Character of the thermal motion of water molecules according to the data on quasielastic incoherent scattering of slow neutrons

The paper discusses the applicability of quasi-crystalline approximation to describing the thermal motion of water molecules in their normal and supercooled states. The problem is subjected to the critical analysis of experimental data on incoherent scattering of slow neutrons based on theories developed by Singwi-Sjolander [1] and Oskotsky [2] modified to duly take into account the limited applicability range of diffusion approximation. The applicability conditions of quasi-crystalline approximation are shown to be consistently satisfied only when water is in supercooled state and within a narrow temperature range above the melting temperature.     

Investigation of hypersonic nozzle flow uniformity using NO fluorescence

Planar laser-induced fluorescence visualisation is used to investigate nonuniformities in the flow of a hypersonic conical nozzle. Possible causes for the nonuniformity are outlined and investigated, and the problem is shown to be due to a small step at the nozzle throat. Entrainment of cold boundary layer gas is postulated as the cause of the signal nonuniformity. PACS 47.80.Jk, 47.40.Ki, 47.60.+i     

On the Local Uniqueness of Solutions of Variational Inequalities Under H-Differentiability

In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C ¹ and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C ² and C ¹ nonlinear complementarity problems.